An understanding of the capacity for numerical competence in non- human species could contribute significantly toward clarifying theoretical evolutionary changes in cognitive processing across phyla. In the proposed studies, chimpanzees previously trained on a variety of number-related tasks, including productive and receptive use of Arabic number symbols, will be tested for sensitivity to ordinality. These tasks will require the utilization of transitive inference logical reasoning, and will provide important empirical evidence that the chimpanzee may be capable of true counting, as demonstrated with very young children. These findings, together with previously demonstrated capabilities in the animals for one-to-one correspondence, productive and receptive labelling of homogeneous and heterogeneous arrays, the functional use of numbers, and rudimentary arithmetic processes (addition, identity) would provide critical evidence for a counting explanation for the animals' number-related behaviors. Training will also continue with on-going studies of functional number use (0-5), to include the additional Arabic numbers 6 & 7, as well as studies of rudimentary arithmetic processing in the chimpanzee.